### Abstract

Let (W; S) be a Coxeter system. A W-graph is an encoding of a representation of the corresponding Iwahori-Hecke algebra. Especially important examples include the W-graph corresponding to the action of the Iwahori-Hecke algebra on the Kazhdan-Lusztig basis as well as this graph's strongly connected components (cells). In 2008, Stembridge identified some common features of the Kazhdan-Lusztig graphs ("admissibility") and gave combinatorial rules for detecting admissibleW-graphs. He conjectured, and checked up to n = 9, that all admissible A_{n}-cells are Kazhdan-Lusztig cells. The current paper provides a possible first step toward a proof of the conjecture. More concretely, we prove that the connected subgraphs of A_{n}-cells consisting of simple (i.e. directed both ways) edges do fit into the Kazhdan-Lusztig cells.

Original language | English (US) |
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Pages (from-to) | 313-324 |

Number of pages | 12 |

Journal | Discrete Mathematics and Theoretical Computer Science |

State | Published - Nov 18 2013 |

Event | 25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 - Paris, France Duration: Jun 24 2013 → Jun 28 2013 |

### Keywords

- Dual equivalence graphs
- Iwahori-hecke algebra
- Kazhdan-lusztig cells
- W-graphs
- W-molecules

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## Cite this

*Discrete Mathematics and Theoretical Computer Science*, 313-324.